Michael Carrick’s rejuvenated side never looked back after Sam Greenwood opened the scoring in the first minute of the second half.
Substitute Sammy Silvera completed a deserved win by netting a second in stoppage time and although Jonathan Rowe pulled one back at the death, his eighth goal of the season was no more than a consolation for the struggling hosts.
It was a second home defeat in the space of four days for the Canaries, who have slumped alarmingly after a bright beginning to the season.
After a slow start Boro had the better of a scrappy first half and carved out a number of decent opportunities as the game passed the half-hour mark.
Josh Coburn sent a close-range header straight at George Long after the home goalkeeper had punched a Jonny Howson high into the night sky and then Lukas Engel fired just over after being set up by a glorious crossfield ball from Isaiah Jones.
The visitors went even closer a few minutes later as the hosts carelessly coughed up possession deep inside their own half, allowing Hayden Hackney to bear down on goal but, although his shot beat Long, defender Shane Duffy was behind him to block.
After the recalled Marcelino Nunez had got an early shot on target, Norwich barely threatened despite having plenty of the ball and were booed off by some fans at the break.
The mood of the home faithful hardly improved when Boro took the lead 33 seconds into the second period
following a woefully misplaced pass by defender Dimi Giannoulis.
Hackney nipped in to intercept and sent Coburn racing through and the youngster simply squared for an unmarked Greenwood to slide the ball home with ease.
Norwich responded in spirited fashion, with Nunez cracking a shot against the crossbar after being fed by Giannoulis and Ben Gibson sending a powerful header inches wide against his former club.
Boro seemed content to soak up the pressure and rely on the occasional counter-attack and as the half wore Norwich struggled to get a clear sight of goal themselves.
It was the visitors who wrapped up the points in the second minute of stoppage time when substitute Silvera picked up a loose ball and skipped into the area before guiding a low shot into the bottom corner.
Rowe produced a tremendous finish from a tight angle to reduce the arrears in the ninth minute of added time but there was no time for another Norwich response.